Market activity is expected to return to usual levels on Tuesday as traders in the United States return from a public holiday.
At 0746 GMT, the rouble was 0.2pc stronger against the dollar at 64.19 and had gained 0.2pc to trade at 70.77 versus the euro.
Brent crude oil, a global benchmark for Russia's main export, was down 0.5pc at $59.1 a barrel.
As optimism over China-U.S. trade talks fades, the attention of global markets may turn to the risk in Britain of a disorderly exit from the European Union, ahead of crucial talks on Thursday and Friday.
Inflows into OFZ treasury bonds were driven up by strong indications from the central bank last week and on Monday that it could cut its key rate as soon as the next rate-setting meeting on Oct. 25.
Market analyst Mikhail Poddubsky of Promsvyazbank expected the rouble to remain between 64.0 and 64.5 in the short term.
"To some extent, the inflow of speculative capital into the Russian debt market may support the Russian currency," said Poddubsky.
Russian stock indexes were up.
The dollar-denominated RTS index was up 0.4pc to 1326.9 points. The rouble-based MOEX Russian index was 0.3pc higher at 2704.6 points.
The Moscow Exchange itself made early gains of 1.2pc as its new chief executive officer, Yury Denisov, gave his first interview since taking the role in May and announced a higher threshold for dividend payments.